Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes and angle $\left(\frac{3 \pi}{4}\right)^{\mathrm{C}}$ with positive $\mathrm{X}$-axis, then $f^{\prime}(3)$ is equal to
MathematicsApplication of DerivativesMHT CETMHT CET 2022 (06 Aug Shift 2)
Options:
  • A $-1$
  • B $1$
  • C $\frac{4}{3}$
  • D $-\frac{3}{4}$
Solution:
2047 Upvotes Verified Answer
The correct answer is: $1$
$\begin{aligned} & \text { Slope of normal }=\frac{-1}{f^{\prime}(x)} \\ & \Rightarrow \tan \left(\frac{3 \pi}{4}\right)=\frac{-1}{f^{\prime}(3)} \\ & \Rightarrow-1=\frac{-1}{f^{\prime}(3)} \\ & \Rightarrow f^{\prime}(3)=1\end{aligned}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.